Size of a bee swarm from its fractions

From a swarm of bees, a number equal to the square root of half the swarm settles on a bush, and eight-ninths of the swarm stays behind. The remaining two bees, one male and one female, fly off and are caught by a bird. How many bees were in the swarm originally?

72. With $n$ bees, $\sqrt{n/2}+\tfrac{8n}{9}+2=n$. Setting $n=2k^2$ turns this into $2k^2-9k-18=0$, so $k=6$ and $n=72$ (the other root gives a non-integer swarm). Check: $6+64+2=72$.